# Integration Question

1. May 7, 2010

1. The problem statement, all variables and given/known data
Hi, I know this is a mechanics question, but I don't think the actual problem I have with it involves any mechanics, it's just integration techniques.

Find the deflection angle of a particle moving in the following repulsive central field:

U = α/r², α > 0

2. Relevant equations

Use the formula $$\int$$1/(x√(x² - 1))dx = π/2 (π = pi)
where the integral limits are 1 (lower) and ∞ (upper)

3. The attempt at a solution
Hi everyone, here's what I've done so far:

I use the formula χ = | π - 2ϕ_0 |, where χ is the angle of deflection

and then ϕ_0 = $$\int$$ (ρ/r²√(1 - ρ²/r² - U(r)/E) dr

where the integral limits are r_min (lower) and ∞ (upper)

I am trying to turn this into the form given in the question to apply the formula.

First I factor out a 1/r from inside the square root and sub in the value for U(r):

ϕ_0 = $$\int$$ (ρ/r√(r² - (ρ² + α/E)) dr

But this is where I get stuck, as I can't see how to turn the (ρ² + α/E) into a 1. Can anyone please point me in the right direction?

Thanks in advance for any help! :)

2. May 7, 2010